DAVOS, Switzerland (Reuters) - A British PR guru who is leading a campaign for a "soft" Brexit says all is not lost despite Prime Minister Theresa May's insistence on a clean break from the EU single market.

Roland Rudd's political and business links are near unparalleled: he advised former Prime Minister Tony Blair and counts David Cameron as a friend, and his financial PR firm Finsbury represents about a quarter of FTSE 100 companies.

He also heads the Open Britain group, which is campaigning for Britain to retain as close ties as possible with the European Union - particularly retaining membership of the single market.

But on Tuesday, May put paid to the idea, saying Britain would quit the market when it leaves the EU to be able to control the high rates of immigration that spurred millions of voters to choose Brexit.

Rudd has not abandoned hope.

He conceded May's speech had forced him to move his own goal posts and now try to get an agreement that he describes would be as good as being in the single market.

"I still think there is a lot to fight for. The prime minister has articulated her early view about the direction of travel but how we get there, in what form and how it finally gets driven is all up for discussion," he told Reuters on the sidelines of the World Economic Forum in Davos, Switzerland.

In practical terms, he said he would push for a transitional period for many companies to avoid a cliff edge and adjust to new and uncertain trading conditions.

While denying that he is a "mouthpiece" for the companies Finsbury represents, he said he was "cognizant of what a lot of business wants because that's my day-to-day job".

"What I would say is that they are very focused on the transitory arrangement, because she (May) was being very optimistic and saying, look we want to get this done in two years," he said.

British bank Barclays said on Thursday that it was looking for a three-year transition period for the financial sector.

Rudd also rejected the idea of curbing migration by applying existing controls for non-EU citizens to those from the bloc, potentially putting him at odds with Amber Rudd - the British interior minister and his sister.

Instead he said he would press for some kind of flexible overall cap on immigration numbers.

"No one voted to stop immigration, they said they wanted to control immigration," he said.

INSIDER ON THE OUTSIDE

Rudd, a peerless networker whose close ties to government were the envy of competitors and whose dinner parties are a roll call for the great and good of London society, is at home in Davos, where the world's political and business elites have gathered this week.

But he finds himself in an unfamiliar, and perhaps unsettling, position in Britain.

He is on the opposite side of the debate from a prime minister he does not have a close relationship with, and the establishment he is so deeply plugged into has been rejected by voters in a populist wave sweeping the West.

"What I think is very important, is that you've got to engage with new administrations, with new politicians but you don't have to completely upend your own principles and your own deep held views," he said.

"So I am not going to pretend that I am not anything other than a liberal progressive who does believe in a sort of liberal global world order which is under huge threat. But I am not going to abandon it because it is in vogue to abandon it."

With the opposition Labour Party in disarray over its Brexit stance and liberal ideas of a free market and globalization in retreat, Rudd fears that May could be given too much of a free hand to dictate terms in some of the most complicated talks Britain has engaged in since World War Two.

In her speech this week, May did offer some comfort to Rudd and other proponents of a soft Brexit when she said she wanted a deal with Brussels that "may take in elements of current single-market arrangements in certain areas" and to have a customs agreement.

Sources close to the government's thinking suggest May could try to get better deals for some parts of the economy, such as the carmaking industry and pharmaceuticals - but Dominic Raab, a lawmaker with the ruling Conservative Party, told Reuters he did not think she was "going to barter bits of the UK economy".

Rudd said it was too early to say whether that was May's game plan, but said his campaign would continue to argue for a very liberal, tolerant society.

"I've always been an optimist so I have moments where I am a little down but I never let them last long."